1. Cook butter in a small heavy saucepan over medium heat, stirring constantly, 8 to 10 minutes or until butter begins to turn golden brown. Remove pan immediately from heat, and pour butter into a small bowl. Cover and chill 1 hour or until butter is cool and begins to solidify.
2. Beat butter at medium speed with an electric mixer until fluffy; gradually add sugar alternately with milk, beginning and ending with sugar. Beat at low speed until well blended after each addition. Stir in vanilla.
GET THE LOOK: Double the frosting recipe. Fit a pastry bag with a basket-weave tip; fill with frosting. Pipe basket-weave pattern around sides of cake, refilling bag as needed. Use a star tip to pipe ruffle around top of cake.